As negotiators and ministers enter the next round of international negotiations on climate change, they face a painful conundrum; domestic politics in the US has made it nigh on impossible for countries to sign a legally binding agreement in Mexico. Yet the need for such an agreement is ever more obvious, as climate impacts accelerate, countries jostle for advantage in the clean technology markets while still burning coal and oil at record speeds; and money begins to flow into a complex series of bilateral and multilateral deals to support action on forests, adaptation and low-carbon development.

In place of a global deal with common rules and a sense of purpose, we are now faced with a bottom-up, ad hoc and chaotic response to a planetary emergency. It is as if we were trying to deal with a deadly pandemic by brewing home-made vaccines.

And with last week's ominous news of a rise in atmospheric methane levels, possibly linked to rapid Arctic warming, the dislocation between the scale of the risk posed by climate change, and the laughably inadequate response of the international community is more obvious than ever.

But while the problem is stark and growing, many campaigners feel as if they are running out of options. If the international process is broken, and we can't fix the problem of climate change without it – what comes next? For some, the answer is to continue throwing energy at the UNFCCC process itself – as if there might be some alchemic substance in the water in Cancún, which will transform political conditions on the ground in Beijing or Washington DC. Nice try, but most of us don't believe in magic.

However, taking umbrage with the UNFCCC, and even with climate change itself, and instead focussing on energy security and green jobs, is an equally inadequate response. Of course, there are synergies between domestic energy security concerns, and the need to reduce emissions. But they are location-specific and limited: and cannot get us where we need to be fast enough, or in a way which is equitable and sustainable. Only international collaboration can do that job.

This leaves those of us who are not prepared to give up – and there are millions of us – with only one choice. We must continue to work for an international deal on climate change. But we must do so in a way which systematically builds the political conditions necessary for such a deal, in the places where it matters – in capitals.

Firstly, we must remain steadfast in defending the climate imperative for action; and rational and lucid in explaining the science underpinning this. Because no other logic will prevent the world's economies burning up all the world's fossil fuels until they are gone.

Secondly, we need to identify the specific failures of good faith that threaten to sour the atmosphere in Cancún and beyond – and dismantle them. Governments must be made to deliver on the emissions reduction and financial promises they made in Copenhagen – including the $30bn of fast-start finance pledged by rich countries for action on adaptation, forests and clean energy.

By insisting on delivery, we can help politicians make the limited, but nonetheless vital progress that is possible in Cancún. With a fair wind and goodwill, that could include formal recognition of the positive elements of the Copenhagen Accord – including a global goal to limit temperature rises to below 2 degrees, and to mobilise $100bn of climate finance annually, by 2020. It also could include meaningful agreements on forests, adaptation and technology. And it might even include a provisional agreement to retain the Kyoto Protocol, as part of a plan for a more comprehensive legally binding deal in future.

But ultimately, to get the real deal – the one which sets the world on a rapid path towards a low-carbon economy – we will have to tackle the stranglehold of high-carbon businesses on decision making in the world's richest countries. This means challenging them when they go after new oil beneath Canadian forests or in the seas of the Arctic; or where they plan to lock our economies into a whole new, lethal generation of coal-fired power. It means challenging them in boardrooms, where they use business models which project global temperature rises of six degrees. And it means demanding an end to the subsidies – national and international – which perpetuate their death grip on the global energy economy.

Eventually, the world will shake Big Carbon off from around its ankles, and walk free. But for now, climate campaigners have a simple job – to bring that moment forward, minute by minute, and day by day, using every non-violent means in their power.